Question

If y = sin x and x changes from π/2 to 22/14, what is the approximate change in y ?

Answer 1

\[\text { Let }: \]

\[ x = \frac{\pi}{2}\]

\[ x + \bigtriangleup x = \frac{22}{14}\]

\[ \Rightarrow dx = \bigtriangleup x = \frac{22}{14} - \frac{\pi}{2} = 0\]

\[\text { Now, y } = \sin x\]

\[ \Rightarrow \frac{dy}{dx} = \cos x\]

\[ \Rightarrow \left( \frac{dy}{dx} \right)_{x = \frac{\pi}{2}} = \cos\left( \frac{\pi}{2} \right) = 0\]

\[ \therefore ∆ y = \frac{dy}{dx} ∆ x = 0 \times 0 = 0\]

\[ \Rightarrow \bigtriangleup y = 0\]

Hence, there is no change in the value of y.